- Explicitely passed pred_subset_eq and pred_equals_eq as an argument to the
to_set and to_pred attributes, because it is no longer applied automatically
- Manually applied predicate1I in proof of accp_subset, because it is no longer
part of the claset
- Replaced psubset_def by less_le
(*<*)
theory Plus imports Main begin
(*>*)
text{*\noindent Define the following addition function *}
consts add :: "nat \<Rightarrow> nat \<Rightarrow> nat"
primrec
"add m 0 = m"
"add m (Suc n) = add (Suc m) n"
text{*\noindent and prove*}
(*<*)
lemma [simp]: "!m. add m n = m+n"
apply(induct_tac n)
by(auto)
(*>*)
lemma "add m n = m+n"
(*<*)
by(simp)
end
(*>*)